Finite Group Databasebeta

C2×(C22⋊D191)⋊C8 #37581190

order24448
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×(C22⋊D191)⋊C8

Splittings

FittingC2×C22⋊C8×C191 ⋊ C2
SylowC191 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC2×C191C23×C8
FrattiniC2×C4C23×D191
FittingC2×C22⋊C8×C191C2
socleC23×C191C22×C4
prime radicalC22×C22⋊D191C4
cosocleC2×C4×C191C24
hypercenterC2×C22⋊C8D191
hypocenterC191C2×C8×D4
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13180);